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Funktsional. Anal. i Prilozhen., 2000, Volume 34, Issue 1, Pages 51–64 (Mi faa282)  

This article is cited in 37 scientific papers (total in 37 papers)

Anisotropic Young Diagrams and Jack Symmetric Functions

S. V. Kerov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: We study the Young lattice with the edge multiplicities $\varkappa_\alpha(\lambda,\Lambda)$ arising in the simplest Pieri formula for Jack symmetric polynomials $P_\lambda(x;\alpha)$ with parameter $\alpha$. A new proof of Stanley's $\alpha$-version of the hook formula is given. We also prove the formula
$$ \sum_\Lambda (c_\alpha(b)+u)(c_\alpha(b)+v)\varkappa_\alpha(\lambda,\Lambda)\varphi(\Lambda)= (n\alpha+uv)\varphi(\lambda), $$
where $\varphi(\lambda)=\prod_{b\in\lambda}(a(b)\alpha+l(b)+1)^{-1}$ and $c_\alpha(b)$ is the $\alpha$-contents of the new box $b=\Lambda\setminus\lambda$.

DOI: https://doi.org/10.4213/faa282

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English version:
Functional Analysis and Its Applications, 2000, 34:1, 41–51

Bibliographic databases:

UDC: 519.217+517.986
Received: 05.05.1998

Citation: S. V. Kerov, “Anisotropic Young Diagrams and Jack Symmetric Functions”, Funktsional. Anal. i Prilozhen., 34:1 (2000), 51–64; Funct. Anal. Appl., 34:1 (2000), 41–51

Citation in format AMSBIB
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\by S.~V.~Kerov
\paper Anisotropic Young Diagrams and Jack Symmetric Functions
\jour Funktsional. Anal. i Prilozhen.
\yr 2000
\vol 34
\issue 1
\pages 51--64
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1756734}
\zmath{https://zbmath.org/?q=an:0959.05116}
\transl
\jour Funct. Anal. Appl.
\yr 2000
\vol 34
\issue 1
\pages 41--51
\crossref{https://doi.org/10.1007/BF02467066}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Borodin, A, “Distributions on partitions, point processes, and the hypergeometric kernel”, Communications in Mathematical Physics, 211:2 (2000), 335  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Regev, A, “S-infinity representations and combinatorial identities”, Transactions of the American Mathematical Society, 353:11 (2001), 4371  crossref  mathscinet  zmath  isi
    3. G. I. Olshanskii, “Probability Measures on Dual Objects to Compact Symmetric Spaces and Hypergeometric Identities”, Funct. Anal. Appl., 37:4 (2003), 281–301  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. S. V. Kerov, “Multidimensional hypergeometric distribution, and characters of the unitary group”, J. Math. Sci. (N. Y.), 129:2 (2005), 3697–3729  mathnet  crossref  mathscinet  zmath
    5. Olshanski, C, “An introduction to harmonic analysis on the infinite symmetric group”, Asymptotic Combinatorics With Applications To Mathematical Physics, 1815 (2003), 127  crossref  mathscinet  zmath  isi
    6. Olshanski G., “Point processes related to the infinite symmetric group”, Orbit Method in Geometry and Physics - in Honor of A.A. Kirillov, Progress in Mathematics, 213, 2003, 349–393  mathscinet  zmath  isi
    7. Fulman, J, “Stein's method, Jack measure, and the Metropolis algorithm”, Journal of Combinatorial Theory Series A, 108:2 (2004), 275  crossref  mathscinet  zmath  isi  scopus
    8. Kerov, S, “Harmonic analysis on the infinite symmetric group”, Inventiones Mathematicae, 158:3 (2004), 551  crossref  mathscinet  zmath  adsnasa  isi  scopus
    9. Lassalle, M, “Jack polynomials and some identities for partitions”, Transactions of the American Mathematical Society, 356:9 (2004), 3455  crossref  mathscinet  zmath  isi  scopus
    10. Borodin, A, “Z-measures on partitions and their scaling limits”, European Journal of Combinatorics, 26:6 (2005), 795  crossref  mathscinet  zmath  isi  scopus
    11. Fulman, J, “An inductive proof of the berry-esseen theorem for character ratios”, Annals of Combinatorics, 10:3 (2006), 319  crossref  mathscinet  zmath  isi  scopus
    12. Fulman, J, “Martingales and character ratios”, Transactions of the American Mathematical Society, 358:10 (2006), 4533  crossref  mathscinet  zmath  isi  scopus
    13. Borodin, A, “Giambelli compatible point processes”, Advances in Applied Mathematics, 37:2 (2006), 209  crossref  mathscinet  zmath  isi  scopus
    14. Borodin, A, “Markov processes on partitions”, Probability Theory and Related Fields, 135:1 (2006), 84  crossref  mathscinet  zmath  isi  scopus
    15. Nekrasov N.A., Okounkov A., “Seiberg-Witten theory and random partitions”, Unity of Mathematics - IN HONOR OF THE NINETIETH BIRTHDAY OF I.M. GELFAND, Progress in Mathematics, 244, 2006, 525–596  crossref  mathscinet  zmath  isi  scopus
    16. Marshakov, A, “Extended Seiberg-Witten theory and integrable hierarchy”, Journal of High Energy Physics, 2007, no. 1, 104  crossref  mathscinet  isi  scopus
    17. Strahov, E, “Matrix Kernels for Measures on Partitions”, Journal of Statistical Physics, 133:5 (2008), 899  crossref  mathscinet  zmath  adsnasa  isi  scopus
    18. Fulman, J, “Stein's method and random character ratios”, Transactions of the American Mathematical Society, 360:7 (2008), 3687  crossref  mathscinet  zmath  isi  scopus
    19. Lassalle, M, “Jack polynomials and free cumulants”, Advances in Mathematics, 222:6 (2009), 2227  crossref  mathscinet  zmath  isi  scopus
    20. L. Petrov, “Random walks on strict partitions”, J. Math. Sci. (N. Y.), 168:3 (2010), 437–463  mathnet  crossref
    21. Strahov, E, “Z-measures on partitions related to the infinite Gelfand pair (S(2 infinity), H(infinity))”, Journal of Algebra, 323:2 (2010), 349  crossref  mathscinet  zmath  isi  scopus
    22. Olshanski G., “Plancherel averages: Remarks on a paper by Stanley”, Electronic Journal of Combinatorics, 17:1 (2010), R43  mathscinet  zmath  isi
    23. Strahov E., “The z-measures on partitions, Pfaffian point processes, and the matrix hypergeometric kernel”, Advances in Mathematics, 224:1 (2010), 130–168  crossref  mathscinet  zmath  isi  scopus
    24. Fulman J., Goldstein L., “Zero Biasing and Jack Measures”, Combinatorics Probability & Computing, 20:5 (2011), 753–762  crossref  mathscinet  zmath  isi  scopus
    25. Kitanine N., Kozlowski K.K., Maillet J.M., Slavnov N.A., Terras V., “A Form Factor Approach to the Asymptotic Behavior of Correlation Functions in Critical Models”, J. Stat. Mech.-Theory Exp., 2011, P12010  crossref  isi  scopus
    26. Kitanine N., Kozlowski K.K., Maillet J.M., Slavnov N.A., Terras V., “Form Factor Approach to Dynamical Correlation Functions in Critical Models”, J. Stat. Mech.-Theory Exp., 2012, P09001  crossref  mathscinet  isi  elib  scopus
    27. N. A. Slavnov, “Asymptotic expansions for correlation functions of one-dimensional bosons”, Theoret. and Math. Phys., 174:1 (2013), 109–121  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    28. Bufetov A., “Kerov's Interlacing Sequences and Random Matrices”, J. Math. Phys., 54:11 (2013), 113302  crossref  mathscinet  zmath  adsnasa  isi  scopus
    29. Lassalle M., “Class Expansion of Some Symmetric Functions in Jucys-Murphy Elements”, J. Algebra, 394 (2013), 397–443  crossref  mathscinet  zmath  isi  elib  scopus
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    31. J. Math. Sci. (N. Y.), 215:6 (2016), 755–768  mathnet  crossref  mathscinet
    32. Dolega M., Feray V., “Gaussian fluctuations of Young diagrams and structure constants of Jack characters”, Duke Math. J., 165:7 (2016), 1193–1282  crossref  mathscinet  zmath  isi  scopus
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  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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